Chanel Lambskin - how do I clean it/care for it?

Hello, just got this pre-loved beauty and touched up the corners using Saphir Renovating Repair Cream (which worked great - see pics) but am not sure what to use for the white portion of the bag. I'm not sure if the marks are scuff or scratches, but I tried Cadillac Cleaner/Conditioner and a white eraser (separately) with no effects. I tried to research it but I'm not even sure what the material/coating is used to create this white color on top of the black leather, so it's hard to find info. Anyone have any ideas?

I know I can take it to a cobbler or submit it to a spa, but if there's something relatively simple I can do myself to touch it up, I'd rather go that route. If not, I may just live with it as-is for now. Thank you in advance for any suggestions!

BTW - TOTALLY recommend the Saphir Renovating Repair Cream per these tutorials:

 

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